A general introduction to trajectory planning is provided in [1]}. The authors of [2]} first introduce the method of minimum-snap that leverages quadrotors' differential flatness and apply monomial polynomial parametrization to the planning trajectory. The method uses snap information to build the cost function and formulate the optimization problem in the form of a convex QP. The problem can be solved efficiently with off-the-shelf solvers, making it possible for real-time onboard motion planning. Moreover, the QP formulation permits more features of trajectory planning to be integrated using equality or inequality constraints. Based on this formulation, the authors of [3]} replace monomial polynomials with Bernstein polynomials to confine the whole trajectory in a convex hull with safety assurance. Another variant uses B-spline instead of monomial polynomials to include curvature constraints on the planned trajectory [4]}.
